COHOMOLOGICAL ASPECTS OF COMPLETE REDUCIBILITY OF REPRESENTATIONS

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The thesis explores continuous group cohomology of representations from separable locally compact groups on Banach spaces, emphasizing compact groups. It introduces a recursive definition of cohomology to establish vanishing theorems, particularly when certain fixed points exist. The relationship between cohomology of connected Lie groups and their Lie algebras is also examined. Additionally, for cocompact closed subgroups, it demonstrates the injectivity of the restriction map, linking this to the complete reducibility of representations.